Timeline for answer to Light rays bouncing in twisted tubes by Anton Petrunin
Current License: CC BY-SA 3.0
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| Jul 16, 2011 at 11:21 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 21:31 | comment | added | Gerhard Paseman | Joseph: COnsider your example above where you have a near miss. Instead of growing the tube straight, grow it along with the light ray, and have it strike the tube at decreasingly smaller angles with the radius of curvature, producing a slight wiggle in the tube. Anton's claim is that the wiggle can be done in a $C^2$ way, and that you only need a finite amount of material (but infinite precision!) to do it. Gerhard "Ask Me About System Design" Paseman, 2011.07.15 | |
| Jul 15, 2011 at 20:31 | comment | added | Joseph O'Rourke | I hesitate to reveal my confusion, but I do not understand this indubitably clever construction. The key phrase I do not understand is, "the ray approach a direction tangent to one of the discs." I can see how the angle of the ray and a disk (what is "one of the discs"?) can be made arbitrarily small, but I do not see how this captures the ray. And I am wary of the word "approach." Any further elucidation would be appreciated! | |
| Jul 15, 2011 at 20:04 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 14:11 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 13:52 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 12:31 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 12:22 | history | edited | Anton Petrunin | CC BY-SA 3.0 |
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| Jul 15, 2011 at 12:13 | history | answered | Anton Petrunin | CC BY-SA 3.0 |